x+3/2x+(x+45)+(2x-90)+90=540

Solution for x+3/2x+(x+45)+(2x-90)+90=540 equation:

x+3/2x+(x+45)+(2x-90)+90=540

We move all terms to the left:

x+3/2x+(x+45)+(2x-90)+90-(540)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/2x+(x+45)+(2x-90)-450=0

We get rid of parentheses

x+3/2x+x+2x+45-90-450=0

We multiply all the terms by the denominator


x*2x+x*2x+2x*2x+45*2x-90*2x-450*2x+3=0

Wy multiply elements

2x^2+2x^2+4x^2+90x-180x-900x+3=0

We add all the numbers together, and all the variables

8x^2-990x+3=0

a = 8; b = -990; c = +3;
Δ = b2-4ac
Δ = -9902-4·8·3
Δ = 980004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{980004}=\sqrt{4*245001}=\sqrt{4}*\sqrt{245001}=2\sqrt{245001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-990)-2\sqrt{245001}}{2*8}=\frac{990-2\sqrt{245001}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-990)+2\sqrt{245001}}{2*8}=\frac{990+2\sqrt{245001}}{16}
$